1 /* 2 * Copyright (c) 1989 The Regents of the University of California. 3 * All rights reserved. 4 * 5 * This code is derived from software contributed to Berkeley by 6 * Landon Curt Noll. 7 * 8 * Redistribution and use in source and binary forms are permitted 9 * provided that the above copyright notice and this paragraph are 10 * duplicated in all such forms and that any documentation, 11 * advertising materials, and other materials related to such 12 * distribution and use acknowledge that the software was developed 13 * by the University of California, Berkeley. The name of the 14 * University may not be used to endorse or promote products derived 15 * from this software without specific prior written permission. 16 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR 17 * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED 18 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. 19 */ 20 21 #ifndef lint 22 char copyright[] = 23 "@(#) Copyright (c) 1989 The Regents of the University of California.\n\ 24 All rights reserved.\n"; 25 #endif /* not lint */ 26 27 #ifndef lint 28 static char sccsid[] = "@(#)primes.c 5.3 (Berkeley) 02/02/90"; 29 #endif /* not lint */ 30 31 /* 32 * primes - generate a table of primes between two values 33 * 34 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo 35 * 36 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\ 37 * 38 * usage: 39 * primes [start [stop]] 40 * 41 * Print primes >= start and < stop. If stop is omitted, 42 * the value 4294967295 (2^32-1) is assumed. If start is 43 * omitted, start is read from standard input. 44 * 45 * Prints "ouch" if start or stop is bogus. 46 * 47 * validation check: there are 664579 primes between 0 and 10^7 48 */ 49 50 #include <stdio.h> 51 #include <math.h> 52 #include <memory.h> 53 #include <ctype.h> 54 #include "primes.h" 55 56 /* 57 * Eratosthenes sieve table 58 * 59 * We only sieve the odd numbers. The base of our sieve windows are always 60 * odd. If the base of table is 1, table[i] represents 2*i-1. After the 61 * sieve, table[i] == 1 if and only iff 2*i-1 is prime. 62 * 63 * We make TABSIZE large to reduce the overhead of inner loop setup. 64 */ 65 char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */ 66 67 /* 68 * prime[i] is the (i-1)th prime. 69 * 70 * We are able to sieve 2^32-1 because this byte table yields all primes 71 * up to 65537 and 65537^2 > 2^32-1. 72 */ 73 extern ubig prime[]; 74 extern ubig *pr_limit; /* largest prime in the prime array */ 75 76 /* 77 * To avoid excessive sieves for small factors, we use the table below to 78 * setup our sieve blocks. Each element represents a odd number starting 79 * with 1. All non-zero elements are factors of 3, 5, 7, 11 and 13. 80 */ 81 extern char pattern[]; 82 extern int pattern_size; /* length of pattern array */ 83 84 #define MAX_LINE 255 /* max line allowed on stdin */ 85 86 char *read_num_buf(); /* read a number buffer */ 87 void primes(); /* print the primes in range */ 88 char *program; /* our name */ 89 90 main(argc, argv) 91 int argc; /* arg count */ 92 char *argv[]; /* args */ 93 { 94 char buf[MAX_LINE+1]; /* input buffer */ 95 char *ret; /* return result */ 96 ubig start; /* where to start generating */ 97 ubig stop; /* don't generate at or above this value */ 98 99 /* 100 * parse args 101 */ 102 program = argv[0]; 103 start = 0; 104 stop = BIG; 105 if (argc == 3) { 106 /* convert low and high args */ 107 if (read_num_buf(NULL, argv[1]) == NULL) { 108 fprintf(stderr, "%s: ouch\n", program); 109 exit(1); 110 } 111 if (read_num_buf(NULL, argv[2]) == NULL) { 112 fprintf(stderr, "%s: ouch\n", program); 113 exit(1); 114 } 115 if (sscanf(argv[1], "%ld", &start) != 1) { 116 fprintf(stderr, "%s: ouch\n", program); 117 exit(1); 118 } 119 if (sscanf(argv[2], "%ld", &stop) != 1) { 120 fprintf(stderr, "%s: ouch\n", program); 121 exit(1); 122 } 123 124 } else if (argc == 2) { 125 /* convert low arg */ 126 if (read_num_buf(NULL, argv[1]) == NULL) { 127 fprintf(stderr, "%s: ouch\n", program); 128 exit(1); 129 } 130 if (sscanf(argv[1], "%ld", &start) != 1) { 131 fprintf(stderr, "%s: ouch\n", program); 132 exit(1); 133 } 134 135 } else { 136 /* read input until we get a good line */ 137 if (read_num_buf(stdin, buf) != NULL) { 138 139 /* convert the buffer */ 140 if (sscanf(buf, "%ld", &start) != 1) { 141 fprintf(stderr, "%s: ouch\n", program); 142 exit(1); 143 } 144 } else { 145 exit(0); 146 } 147 } 148 if (start > stop) { 149 fprintf(stderr, "%s: ouch\n", program); 150 exit(1); 151 } 152 primes(start, stop); 153 exit(0); 154 } 155 156 /* 157 * read_num_buf - read a number buffer from a stream 158 * 159 * Read a number on a line of the form: 160 * 161 * ^[ \t]*\(+?[0-9][0-9]\)*.*$ 162 * 163 * where ? is a 1-or-0 operator and the number is within \( \). 164 * 165 * If does not match the above pattern, it is ignored and a new 166 * line is read. If the number is too large or small, we will 167 * print ouch and read a new line. 168 * 169 * We have to be very careful on how we check the magnitude of the 170 * input. We can not use numeric checks because of the need to 171 * check values against maximum numeric values. 172 * 173 * This routine will return a line containing a ascii number between 174 * 0 and BIG, or it will return NULL. 175 * 176 * If the stream is NULL then buf will be processed as if were 177 * a single line stream. 178 * 179 * returns: 180 * char * pointer to leading digit or + 181 * NULL EOF or error 182 */ 183 char * 184 read_num_buf(input, buf) 185 FILE *input; /* input stream or NULL */ 186 char *buf; /* input buffer */ 187 { 188 static char limit[MAX_LINE+1]; /* ascii value of BIG */ 189 static int limit_len; /* digit count of limit */ 190 int len; /* digits in input (excluding +/-) */ 191 char *s; /* line start marker */ 192 char *d; /* first digit, skip +/- */ 193 char *p; /* scan pointer */ 194 char *z; /* zero scan pointer */ 195 196 /* form the ascii value of SEMIBIG if needed */ 197 if (!isascii(limit[0]) || !isdigit(limit[0])) { 198 sprintf(limit, "%ld", SEMIBIG); 199 limit_len = strlen(limit); 200 } 201 202 /* 203 * the search for a good line 204 */ 205 if (input != NULL && fgets(buf, MAX_LINE, input) == NULL) { 206 /* error or EOF */ 207 return NULL; 208 } 209 do { 210 211 /* ignore leading whitespace */ 212 for (s=buf; *s && s < buf+MAX_LINE; ++s) { 213 if (!isascii(*s) || !isspace(*s)) { 214 break; 215 } 216 } 217 218 /* object if - */ 219 if (*s == '-') { 220 fprintf(stderr, "%s: ouch\n", program); 221 continue; 222 } 223 224 /* skip over any leading + */ 225 if (*s == '+') { 226 d = s+1; 227 } else { 228 d = s; 229 } 230 231 /* note leading zeros */ 232 for (z=d; *z && z < buf+MAX_LINE; ++z) { 233 if (*z != '0') { 234 break; 235 } 236 } 237 238 /* scan for the first non-digit/non-plus/non-minus */ 239 for (p=d; *p && p < buf+MAX_LINE; ++p) { 240 if (!isascii(*p) || !isdigit(*p)) { 241 break; 242 } 243 } 244 245 /* ignore empty lines */ 246 if (p == d) { 247 continue; 248 } 249 *p = '\0'; 250 251 /* object if too many digits */ 252 len = strlen(z); 253 len = (len<=0) ? 1 : len; 254 /* accept if digit count is below limit */ 255 if (len < limit_len) { 256 /* we have good input */ 257 return s; 258 259 /* reject very large numbers */ 260 } else if (len > limit_len) { 261 fprintf(stderr, "%s: ouch\n", program); 262 continue; 263 264 /* carefully check against near limit numbers */ 265 } else if (strcmp(z, limit) > 0) { 266 fprintf(stderr, "%s: ouch\n", program); 267 continue; 268 } 269 /* number is near limit, but is under it */ 270 return s; 271 } while (input != NULL && fgets(buf, MAX_LINE, input) != NULL); 272 273 /* error or EOF */ 274 return NULL; 275 } 276 277 /* 278 * primes - sieve and print primes from start up to and but not including stop 279 */ 280 void 281 primes(start, stop) 282 ubig start; /* where to start generating */ 283 ubig stop; /* don't generate at or above this value */ 284 { 285 register char *q; /* sieve spot */ 286 register ubig factor; /* index and factor */ 287 register char *tab_lim; /* the limit to sieve on the table */ 288 register ubig *p; /* prime table pointer */ 289 register ubig fact_lim; /* highest prime for current block */ 290 291 /* 292 * A number of systems can not convert double values 293 * into unsigned longs when the values are larger than 294 * the largest signed value. Thus we take case when 295 * the double is larger than the value SEMIBIG. *sigh* 296 */ 297 if (start < 3) { 298 start = (ubig)2; 299 } 300 if (stop < 3) { 301 stop = (ubig)2; 302 } 303 if (stop <= start) { 304 return; 305 } 306 307 /* 308 * be sure that the values are odd, or 2 309 */ 310 if (start != 2 && (start&0x1) == 0) { 311 ++start; 312 } 313 if (stop != 2 && (stop&0x1) == 0) { 314 ++stop; 315 } 316 317 /* 318 * quick list of primes <= pr_limit 319 */ 320 if (start <= *pr_limit) { 321 /* skip primes up to the start value */ 322 for (p = &prime[0], factor = prime[0]; 323 factor < stop && p <= pr_limit; 324 factor = *(++p)) { 325 if (factor >= start) { 326 printf("%u\n", factor); 327 } 328 } 329 /* return early if we are done */ 330 if (p <= pr_limit) { 331 return; 332 } 333 start = *pr_limit+2; 334 } 335 336 /* 337 * we shall sieve a bytemap window, note primes and move the window 338 * upward until we pass the stop point 339 */ 340 while (start < stop) { 341 /* 342 * factor out 3, 5, 7, 11 and 13 343 */ 344 /* initial pattern copy */ 345 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ 346 memcpy(table, &pattern[factor], pattern_size-factor); 347 /* main block pattern copies */ 348 for (fact_lim=pattern_size-factor; 349 fact_lim+pattern_size<=TABSIZE; 350 fact_lim+=pattern_size) { 351 memcpy(&table[fact_lim], pattern, pattern_size); 352 } 353 /* final block pattern copy */ 354 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); 355 356 /* 357 * sieve for primes 17 and higher 358 */ 359 /* note highest useful factor and sieve spot */ 360 if (stop-start > TABSIZE+TABSIZE) { 361 tab_lim = &table[TABSIZE]; /* sieve it all */ 362 fact_lim = (int)sqrt( 363 (double)(start)+TABSIZE+TABSIZE+1.0); 364 } else { 365 tab_lim = &table[(stop-start)/2]; /* partial sieve */ 366 fact_lim = (int)sqrt((double)(stop)+1.0); 367 } 368 /* sieve for factors >= 17 */ 369 factor = 17; /* 17 is first prime to use */ 370 p = &prime[7]; /* 19 is next prime, pi(19)=7 */ 371 do { 372 /* determine the factor's initial sieve point */ 373 q = (char *)(start%factor); /* temp storage for mod */ 374 if ((int)q & 0x1) { 375 q = &table[(factor-(int)q)/2]; 376 } else { 377 q = &table[q ? factor-((int)q/2) : 0]; 378 } 379 /* sive for our current factor */ 380 for ( ; q < tab_lim; q += factor) { 381 *q = '\0'; /* sieve out a spot */ 382 } 383 } while ((factor=(ubig)(*(p++))) <= fact_lim); 384 385 /* 386 * print generated primes 387 */ 388 for (q = table; q < tab_lim; ++q, start+=2) { 389 if (*q) { 390 printf("%u\n", start); 391 } 392 } 393 } 394 } 395